1A. The set of points in a plane that are equidistant from a given point is called a _______. A. square B. sphere C. segment D. circle 1B. The given point is called the _______. A. vertex B. center C. axis D. radius 2. The equation x^2+y^2-4x+2y=b describes a circle. Part A. Determine the y-coordinate of the center of the circle. Part B. The radius of the circle is 7 units. What is the value of b in the equation? 3. Point Q lies on ST, where point S is located at (-2, -6) and point T is located at (5, 8). If SQ:QT = 5:2, where is point Q on ST? Give the coordinates for Q. (Use Image #1) 4. The circle with center F is divided into sectors. In circle F, EB is a diameter. The radius of circle F is 3 units. Match each arc length to its subtended central angle. (Use Image #2 & #3)

1A. The set of points in a plane that are equidistant from a given point is called a D. circle

1B. The given point is called the B. center

2. The equation \(x^2 + y^2 - 4x + 2y = b\) describes a circle.

  Part A. Determine the y-coordinate of the center of the circle.

  To complete the square, rewrite the equation:

  \[x^2 - 4x + y^2 + 2y = b\]

  \[x^2 - 4x + 4 + y^2 + 2y + 1 = b + 4 + 1\]

  \[(x - 2)^2 + (y + 1)^2 = b + 5\]

  Comparing this with the standard form of a circle \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center, we can see that the center has coordinates \((2, -1)\).

  Part B. The radius of the circle is \(7\) units. What is the value of \(b\) in the equation?

  \[r^2 = 7^2\]

  \[b + 5 = 49\]

  \[b = 44\]

3. Point \(Q\) lies on \(ST\), where point \(S\) is located at \((-2, -6)\) and point \(T\) is located at \((5, 8)\). If \(SQ:QT = 5:2\), where is point \(Q\) on \(ST\)? Give the coordinates for \(Q\).

  First, find the coordinates of point \(Q\) using the ratio \(5:2\).

  \[Q_x = \frac{5 \cdot T_x + 2 \cdot S_x}{5 + 2}\]

  \[Q_y = \frac{5 \cdot T_y + 2 \cdot S_y}{5 + 2}\]

  Substitute the coordinates of \(S\) and \(T\) into the formulas to find the coordinates of \(Q\).

4. The circle with center \(F\) is divided into sectors. In circle \(F\), \(EB\) is a diameter. The radius of circle \(F\) is \(3\) units. Match each arc length to its subtended central angle. (Use Image #2 & #3)

  Unfortunately, without the specific information from Image #2 & #3, I cannot match the arc lengths to their subtended central angles. If you can provide the details or describe the angles and arcs, I can help you with the matching.